The disclosure relates to an arithmetic processing method and an arithmetic processor, and more particularly relates to an arithmetic processing method and an arithmetic processor of multiplicatively dividing a binary fixed-point number.
A multiplicative division method is one of division methods to obtain an approximation value of a quotient by iteratively solving asymptotic approximation equations to calculate the reciprocal of a dividend, and then multiplying the calculated reciprocal of the dividend by a divisor. Newton-Raphson method and Goldschmidt method are known as typical multiplicative division methods.
In order to converge the approximations with a small number of iterations, both of the above methods use a lookup table (hereinafter referred to as the “LUT”) or the like to acquire a rough approximation value (initial value) of the reciprocal of the divisor. Then, by iteratively performing asymptotic approximation calculations on the acquired initial value, the reciprocal having desired accuracy can be obtained.
Japanese Patent Application Publication No. 02-51732 (Patent Document 1) discloses an example of a technique using such a conventional Newton-Raphson method for floating-point operations.
Here, in the calculation of a binary fixed-point number using the multiplicative division method as described in Patent Document 1, if a value inputted to a unit to generate the reciprocal of a divisor and a value of the reciprocal outputted from the unit are expressed by using the same number of bits, division accuracy is deteriorated particularly in a range where the divisor is large. This is because, when the reciprocal of a large input value is represented by using the range covering the same number of bits, only a small number of bits are outputted as significant bits. In practice, a fixed-point error is about ±(100/2i−1) % where the number of significant bits is i. As described above, the accuracy is significantly deteriorated when the number of significant bits of the fixed-point number is small. As a result, the accuracy of the operation result is also significantly deteriorated unless the initial value of approximation has sufficient accuracy.